It is possible to prove that net bisimilarity \(\sim _n\)  coincides with team bisimilarity over BPP nets [1]},
which in turn coincides with place bisimilarity [2]} on this class of nets.
Interestingly enough, the definition of net bisimulation has some similarities with that of place bisimulation,
as also this relation requires that the size of the related markings is the same and that
the pre-sets of the matching transitions be related. However, on the one hand, on general Petri nets place bisimilarity is strictly
finer than causal-net bisimilarity, as claimed in [3]} and proved in [4]}.
On the other hand, place bisimilarity is decidable [4]}, while the decidability of causal-net bisimilarity
(and so of net bisimilarity) is an open problem for general Petri nets.
Future work will be devoted to prove our conjecture that \(\sim _n\)  is decidable on, possibly unbounded, Petri nets.
Net bisimilarity is decidable on bounded nets, because causal-net bisimilarity has been proved decidable in
(large) exponential time on that class of nets [6]}.
However, we expect that our simpler characterization of \(\sim _{cn}\)  in term of net bisimilarity \(\sim _n\)  may offer some hints towards a
more efficient algorithm, yet exponential as well.
Net bisimilarity is decidable on BPP nets, because on this class of
nets it coincides with team bisimilarity [1]}, [8]}, which is decidable in polynomial time.
